Defining differential operator that acts like curl

As a newbie in using SAGE (experience with Python and Numpy), I was wondering how to define a differential operator that acts like curl (or $\nabla \times \vec F$). The curl for a vector field $\vec F=(F_x,F_y, F_z)$is defined as a determinant $\mathrm{det} (\nabla,\vec F) $. I want to define such operators that act on $F_x, F_y, F_z$ without calculating the determinant a priori. In other words if I was to multiply $\frac {\partial }{\partial x}$ with $F_y$, I would expect to get $\frac{\partial F_y}{\partial x}$
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